[Playground] Keep track of playground state

[Manvi-Agrawal]

Description

• It would be really helpful to store the current state of playground. If someone is navigating some samples, its slightly inconvenient to not being able to go to previous sample by back button.
• This would add a little convivence with local development of katas in watch mode. Typically, someone is developing kata and its slightly annoying to go to desired kata via side-bar navigation.
• As a bonus, it would be good if can generate links to tasks within the sections of kata since some katas might have 8-10 tasks.

Describe alternatives you've considered

• For samples/katas, we can use side bar navigation.
• During local development of katas, we can modify the index.json list and samples.mjs list so that we dont need to scoll down further.

Additional context

• I had this issue earlier in mind but I thought MathJax kata preview fixes #1508 fixed this navigation in playground. I realized from PR description of Support themes in kata previews #1798 that we have a kata viewer in addition to playground and improvements were done there.
• I have something working to support "katas", "samples" and "doc" navigation. Navigation within kata needs to be worked upon.